Key Concepts
- The x-intercept of a function is where the graph crosses the x-axis (that is, when (y = 0)).
- The y-intercept is where the function crosses the y-axis ((x = 0)).
- Functions can be analyzed for intervals of increase and decrease.
Skills Covered
- Identifying x- and y-intercepts from a given graph and their meaning in real-world problems.
- Finding function values from a graph.
- Understanding function behavior by looking at key points.
- Finding intervals where a function increases or decreases.
Example Problems
- A projectile follows (h(t) = -5t^2 + 20t + 30). Find when it hits the ground.
- Identify the interval where (f(x) = x^3 - 6x^2 + 9x) is increasing.